{"id":209294,"date":"2024-03-21T14:07:09","date_gmt":"2024-03-21T14:07:09","guid":{"rendered":"https:\/\/www.electricity-magnetism.org\/%e4%bd%8d%e7%9b%b8%e7%b5%b6%e7%b8%81%e4%bd%93%e3%81%ae%e5%85%ac%e5%bc%8f-%e6%a6%82%e8%a6%81%e3%81%a8%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95\/"},"modified":"2024-05-17T15:10:09","modified_gmt":"2024-05-17T15:10:09","slug":"%e4%bd%8d%e7%9b%b8%e7%b5%b6%e7%b8%81%e4%bd%93%e3%81%ae%e5%85%ac%e5%bc%8f-%e6%a6%82%e8%a6%81%e3%81%a8%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.electricity-magnetism.org\/ja\/%e4%bd%8d%e7%9b%b8%e7%b5%b6%e7%b8%81%e4%bd%93%e3%81%ae%e5%85%ac%e5%bc%8f-%e6%a6%82%e8%a6%81%e3%81%a8%e8%a8%88%e7%ae%97%e6%96%b9%e6%b3%95\/","title":{"rendered":"\u4f4d\u76f8\u7d76\u7e01\u4f53\u306e\u516c\u5f0f | \u6982\u8981\u3068\u8a08\u7b97\u65b9\u6cd5"},"content":{"rendered":"

\u4f4d\u76f8\u7d76\u7e01\u4f53\u306e\u7279\u6027\u3068\u8a08\u7b97\u65b9\u6cd5\u3092\u7c21\u6f54\u306b\u89e3\u8aac\u3002\u5185\u90e8\u306f\u7d76\u7e01\u6027\u3001\u8868\u9762\u306f\u91d1\u5c5e\u6027\u306e\u7279\u6b8a\u306a\u6750\u6599\u306b\u3064\u3044\u3066\u7406\u89e3\u3092\u6df1\u3081\u3088\u3046\u3002<\/p>\n

\u4f4d\u76f8\u7d76\u7e01\u4f53\u306e\u516c\u5f0f | \u6982\u8981\u3068\u8a08\u7b97\u65b9\u6cd5<\/h2>\n

\u4f4d\u76f8\u7d76\u7e01\u4f53\uff08topological insulators\uff09\u306f\u8fd1\u5e74\u306e\u7269\u7406\u5b66\u3067\u6ce8\u76ee\u3055\u308c\u3066\u3044\u308b\u6750\u6599\u306e\u4e00\u3064\u3067\u3001\u5f93\u6765\u306e\u7d76\u7e01\u4f53\u3068\u306f\u7570\u306a\u308b\u7279\u6b8a\u306a\u6027\u8cea\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u4f4d\u76f8\u7d76\u7e01\u4f53\u306e\u4f55\u304c\u7279\u5225\u306a\u306e\u304b\u3001\u305d\u3057\u3066\u305d\u306e\u57fa\u672c\u7684\u306a\u516c\u5f0f\u3068\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u7c21\u5358\u306b\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n

\u4f4d\u76f8\u7d76\u7e01\u4f53\u3068\u306f\uff1f<\/h2>\n

\u4f4d\u76f8\u7d76\u7e01\u4f53\u306f\u3001\u5185\u90e8\u3067\u306f\u7d76\u7e01\u4f53\u306e\u3088\u3046\u306b\u96fb\u6c17\u3092\u901a\u3055\u306a\u3044\u304c\u3001\u8868\u9762\u3084\u5883\u754c\u3067\u306f\u91d1\u5c5e\u306e\u3088\u3046\u306b\u96fb\u6c17\u3092\u901a\u3059\u3068\u3044\u3046\u7279\u6b8a\u306a\u6027\u8cea\u3092\u6301\u3061\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4f4d\u76f8\u7d76\u7e01\u4f53\u306e\u5185\u90e8\u3067\u306f\u96fb\u5b50\u304c\u79fb\u52d5\u3067\u304d\u305a\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u30d0\u30f3\u30c9\u306e\u30ae\u30e3\u30c3\u30d7\u304c\u5b58\u5728\u3057\u307e\u3059\u304c\u3001\u8868\u9762\u72b6\u614b\u3067\u306f\u30ae\u30e3\u30c3\u30d7\u304c\u306a\u304f\u3001\u96fb\u5b50\u304c\u81ea\u7531\u306b\u79fb\u52d5\u3057\u307e\u3059\u3002<\/p>\n

\u3053\u306e\u73fe\u8c61\u306f\u3001\u91cf\u5b50\u529b\u5b66\u7684\u52b9\u679c\u306b\u3088\u3063\u3066\u5f15\u304d\u8d77\u3053\u3055\u308c\u3001\u30b9\u30d4\u30f3\u8ecc\u9053\u76f8\u4e92\u4f5c\u7528\u3092\u542b\u3080\u7279\u5b9a\u306e\u6761\u4ef6\u4e0b\u3067\u51fa\u73fe\u3057\u307e\u3059\u3002\u4f4d\u76f8\u7d76\u7e01\u4f53\u306e\u7279\u6027\u306f\u3001\u6b21\u6570\u3084\u30cf\u30df\u30eb\u30c8\u30f3\u6f14\u7b97\u5b50\u306e\u5bfe\u79f0\u6027\u306b\u3088\u308b\u5206\u985e\u304c\u53ef\u80fd\u3067\u3059\u3002<\/p>\n

\u8a08\u7b97\u65b9\u6cd5\u306e\u6982\u8981<\/h2>\n

\u4f4d\u76f8\u7d76\u7e01\u4f53\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u624b\u9806\u304c\u4e00\u822c\u7684\u3067\u3059\uff1a<\/p>\n

    \n
  1. \u30cf\u30df\u30eb\u30c8\u30f3\u6f14\u7b97\u5b50\u306e\u8a2d\u5b9a<\/li>\n
  2. \u30a8\u30cd\u30eb\u30ae\u30fc\u30d0\u30f3\u30c9\u306e\u8a08\u7b97<\/li>\n
  3. \u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u4e0d\u5909\u91cf\u306e\u8a08\u7b97<\/li>\n<\/ol>\n

    \u5177\u4f53\u7684\u306a\u8a08\u7b97\u65b9\u6cd5<\/h2>\n

    \u5b9f\u969b\u306e\u8a08\u7b97\u4f8b\u3068\u3057\u3066\u30012\u6b21\u5143\u7cfb\u306e\u91cf\u5b50\u30b9\u30d4\u30f3\u30db\u30fc\u30eb\u52b9\u679c\u3092\u8003\u3048\u307e\u3059\u3002\u3053\u306e\u7cfb\u3067\u306fBernevig-Hughes-Zhang\u30e2\u30c7\u30eb\u304c\u3088\u304f\u4f7f\u308f\u308c\u307e\u3059\u3002<\/p>\n

    1. \u30cf\u30df\u30eb\u30c8\u30f3\u6f14\u7b97\u5b50\u306e\u8a2d\u5b9a<\/h3>\n

    \u30cf\u30df\u30eb\u30c8\u30f3\u6f14\u7b97\u5b50\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u307e\u3059\uff1a<\/p>\n

    \\[
    \nH = \\epsilon(\\mathbf{k})I_{4} +
    \n\\begin{pmatrix}
    \nh(\\mathbf{k}) & 0 \\\\
    \n0 & h^*(-\\mathbf{k})
    \n\\end{pmatrix}
    \n\\]<\/p>\n

    \u3053\u3053\u3067\u3001$\\epsilon(\\mathbf{k})$\u306f\u6ce2\u6570$\\mathbf{k}$\u306b\u4f9d\u5b58\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u3001$I_{4}$\u306f4\u6b21\u5143\u5358\u4f4d\u884c\u5217\u3001$h(\\mathbf{k})$\u306f\u884c\u5217\u306e\u30d6\u30ed\u30c3\u30af\u3092\u8868\u3057\u307e\u3059\u3002<\/p>\n

    2. \u30a8\u30cd\u30eb\u30ae\u30fc\u30d0\u30f3\u30c9\u306e\u8a08\u7b97<\/h3>\n

    \u30a8\u30cd\u30eb\u30ae\u30fc\u30d0\u30f3\u30c9\u306f\u3001\u30cf\u30df\u30eb\u30c8\u30f3\u6f14\u7b97\u5b50\u306e\u56fa\u6709\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u3067\u8a08\u7b97\u3057\u307e\u3059\u3002\u56fa\u6709\u5024\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u3067\u3001\u30d0\u30f3\u30c9\u69cb\u9020\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n

    \\[
    \nH|\\psi\\rangle = E|\\psi\\rangle
    \n\\]<\/p>\n

    \u3053\u3053\u3067\u3001$|\\psi\\rangle$\u306f\u56fa\u6709\u72b6\u614b\u3001$E$\u306f\u30a8\u30cd\u30eb\u30ae\u30fc\u56fa\u6709\u5024\u3067\u3059\u3002<\/p>\n

    3. \u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u4e0d\u5909\u91cf\u306e\u8a08\u7b97<\/h3>\n

    \u6b21\u306b\u3001\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u4e0d\u5909\u91cf\uff08\u4f8b\u3048\u3070\u3001\u30c1\u30a7\u30eb\u30f3\u6570\u3084$\\mathbb{Z}_2$\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\uff09\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002$\\mathbb{Z}_2$\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u8a08\u7b97\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u884c\u3044\u307e\u3059\uff1a<\/p>\n

    \\[
    \n(-1)^\\nu = \\prod_{i=1}^4 \\delta_{\\Gamma_i}
    \n\\]<\/p>\n

    \\[
    \n\\delta_{\\Gamma_i} = \\frac{\\sqrt{\\text{Pf}[w(\\Gamma_i)]}}{\\sqrt{\\det[w(\\Gamma_i)]}}
    \n\\]<\/p>\n

    \u3053\u3053\u3067\u3001$w$\u306f\u6642\u9593\u53cd\u8ee2\u5bfe\u79f0\u6027\u306e\u30a6\u30a3\u30eb\u30bd\u30f3\u30eb\u30fc\u30d7\u884c\u5217\u3001$\\Gamma_i$\u306f\u7cfb\u306e\u5bfe\u79f0\u70b9\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n

    \u7d50\u8ad6<\/h2>\n

    \u4f4d\u76f8\u7d76\u7e01\u4f53\u306e\u7279\u6027\u3068\u305d\u306e\u8a08\u7b97\u65b9\u6cd5\u306b\u3064\u3044\u3066\u7c21\u5358\u306b\u8aac\u660e\u3057\u307e\u3057\u305f\u3002\u4f4d\u76f8\u7d76\u7e01\u4f53\u306f\u65b0\u3057\u3044\u7269\u6027\u7269\u7406\u306e\u30d5\u30ed\u30f3\u30c6\u30a3\u30a2\u3067\u3042\u308a\u3001\u5c06\u6765\u306e\u96fb\u5b50\u30c7\u30d0\u30a4\u30b9\u306b\u304a\u3051\u308b\u5fdc\u7528\u304c\u671f\u5f85\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u8208\u5473\u3092\u6301\u3063\u305f\u65b9\u306f\u3001\u3055\u3089\u306b\u8a73\u3057\u3044\u5c02\u9580\u66f8\u3084\u8ad6\u6587\u3092\u8aad\u3080\u3053\u3068\u3067\u3001\u3088\u308a\u6df1\u3044\u7406\u89e3\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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